Financial Engineering is a multidisciplinary field involving finance and economics, mathematics, statistics, engineering and computational methods. The emphasis of FE & RM Part II will be on the use of simple stochastic models to (i) solve portfolio optimization problems (ii) price derivative securities in various asset classes including equities and credit and (iii) consider some advanced applications of financial engineering including algorithmic trading and the pricing of real options. We will also consider the role that financial engineering played during the financial crisis.
We hope that students who complete the course and the prerequisite course (FE & RM Part I) will have a good understanding of the "rocket science" behind financial engineering. But perhaps more importantly, we hope they will also understand the limitations of this theory in practice and why financial models should always be treated with a healthy degree of skepticism.

Enseigné par

Martin Haugh

Co-Director, Center for Financial Engineering

Garud Iyengar

Professor

Transcription

In this first module we're going to briefly review securitization. And we will also discuss how CDOs or collateralized debt obligations are constructed from an underlying pool of bonds. We will of course go into CDOs in much greater detail in later modules we'll see how to price them and we will also discuss the infamous Gaussian Copula Model. Recall the securitization is the name given to the process of constructing new securities from the cash-flows, generated by a pool of underlying securities. An we've already seen examples of securitization in the mortgage market. The economic rationale behind securitization is that it enables the construction of new securities, with a broad range of risk profiles. The broad range of investors may therefore be interested in these new securities, even if they have no interest in the underlying securities. And so this results in an increased amount for the underlying cash flows. This in turn insures that the cost-of-capital is reduced for the issuers of the underlying securities. So for example, in the case of mortgage backed securities by introducing the market for mortgage-backed securities. We increase the demand for cash flows that arise from mortgages, so that we can reduce the mortgage rates for homeowners. Credit default obligations are securities that are constructed from an underlying pool of fixed-income securities. They were first issued by banks in the mid 1990s and their issuance was originally motivated by regulatory arbitrage considerations. And that is why they were supplied to the marketplace in the first place, back, as I said, in the mid 1990s. This slide displays a schematic describing the construction of a CDO. We have an underlying pool of bonds, we see them here, we've got 125 bonds. And they form the collateral for the CDO. The CDO is then divided into tranches defined by their attachment points. So their attachment points are these numbers here. 0% to 3%, 3% to 7%. All the way up to say 40% to 100%. So these numbers on the left, 0, 3 up to 40, they're called the lower attachment points. The numbers on the right, 3, 7, 100 are called the the upper attachment points. These are tranches, so we have the equity tranche, we have the mezzanine tranche. We get maybe other tranches and we have a senior sometimes called a super senior tranche up here. So these are tranches which investors can buy, so for example an investor may buy the equity tranche. Let's say he buys the equity tranche for $50, and what will happen is that the investor will ultimately receive $100. Say over the lifetime of the CDO, if none of the bonds in the underlying pool of assets defaults. But if some bonds default, then the equity tranche would have to incur the losses. And that means that the investor in the equity tranche will no longer receive that $100 I mentioned, but maybe they'll only receive $75. Or maybe $50. In fact, the number they receive, will depend on the number of losses in the underlying pool of bonds. In particular, if the losses in the underlying pool of bonds exceeds 3% of the notional, then maybe they'll get nothing. Right because 3% will exceed this 3% upper attachment point here and so the equity tranche will be wiped out. That doesn't mean that the investor in the equity tranche will receive nothing. Because depending on how the deal is structured, they might receive some payments before the losses in the underlying pool of bonds occurs. But basically, the big picture here is that an investor can buy these individual tranches. They'll pay a certain amount of money for it. and then they receive some cash flows associated with these tranches over the lifetime of the CDO. If any losses arise that impacts these tranches, then they will have to pay some sort of payment because of those losses. We'll get into all of these details in later modules. In fact, just as an aside, later we will consider what's called a synthetic CDO. And in that case, you don't buy a tranche for $50, in fact the payments of a synthetic CDO are structured to work like a swap. So that no cash flows take place at the beginning of the trade. The important takeaway for now, is that if you buy the equity tranche, then you are the hook for the first 3% of losses in the underlying bond pool. If you buy the mezzanine tranche then you are on the hook for losses between 3% and 7% of the notional principal of these 125 bonds. So, maybe each of these bonds has a notional of $1. So, then the total notional principal in the underlying pool is $125. Well, you as an investor in the mezzanine chance will be on the hook for 3% to 7% of 125. So any losses beyod 3% will start impacting the maezzanine chance and any loses above 7% wil start impacting the chance above the mezzanine chance. It should be clear then that the equity chance is the riskiest tranche of the CDO. And that's because the equity tranche is on the hook for the first losses that occur in the underlying good bonds. Likewise the senior tranche, sometimes called the super senior tranche as I mentioned earlier, is the least risky tranche in the CDO. Because this tranche only incurs losses after all of the other tranches below it have been effectively wiped out. In other words, the losses have exceeded all of the attachment points, upper attachment points. 3%, 7%, and so on, and have now entered into the senior tranche. Finally, just one comment here. In practice in order to construct the CDO, the banks that might only underline pool of bonds will often construct what's called an SPV. Which stands for special purpose vehicle. This is a legal entity which is bankruptcy remote from the bank that originally holds these bonds. The bonds, the 125 bonds are placed into this special purpose vehicle... And the special purpose vehicle issues the CDO, and the CDO tranches. But we're not going to get into that. This is part of the legal structuring of these, of these CDOs. So this, by the way, is an example, another example, of an asset backed security. You've seen this already in the mortgage backed security market. This is an asset backed security where the assets, the CDOs, are backed by the underlying pool of bonds. If these bonds were instead placed with loans, we would get what's called a collateralized loan obligation. And in fact, this shouldn't be credit, it should be a collateralized loan obligation. So these are securities that are constructed from the underlying pool of loans. The structured credit market was at the heart of the financial crisis. We saw terms like ABS, MBS, CDO and ABS-CDO's, all these terms became standard in the financial. And indeed the mainstream media during the height of the financial crisis. Our introduction to structured credit and CDO's will do several things. Number one it will provide further examples of the securitization process. Number two, it will allow us to introduce the infamous Gaussian Copula Model. Which came in for an awful lot of criticism in the mainstream media as well as the financial media during the financial crisis. We will discuss the difficulties in risk managing structured credit portfolios. We will also emphasize just how crazy some parts of the financial market have become in the lead-up to the financial crisis. Now it's also worth pointing out that the mechanics of how CEOs work have much in common with the mechanics of how a default swaps. And you already have seen credit default swaps. So it's probably worthwhile reviewing and making sure you understand credit default swaps and their mechanics. Before, continuing on with these modules on structured credit and CDO's. One final point I'll mention, is that if we're ever going to control the excesses in the financial system. Then I think we're going to need a much better understanding of finance outside the finance industry, and certainly the whole, the whole area of structured products. Securitization and so on is considered somewhat mysterious to some people who are not in the financial industry. So I think even understanding the mechanics of securitization, the risks of these new securities is important for people who don't work in finance. But for politicians, journalists, lawyers and so on. So, I think that's another benefit of studying securitization, and studying CDO's as we're going to do in the next several modules.